Rogue waves for a coupled nonlinear Schrödinger system in a multi-mode fibre. Issue 19 (27th October 2016)

• Record Type: Journal Article
• Authors: Li, Hui-Min; Tian, Bo; Wang, Deng-Shan; Sun, Wen-Rong; Xie, Xi-Yang; Liu, Lei
• Is Part Of: Journal of modern optics. Volume 63:Issue 19(2016)
• Page Start: 1924
• Page End: 1931
• Publication Date: 2016-10-27
• Subjects: Optical fibre -- coupled nonlinear Schrödinger system -- generalized Darboux transformation -- gauge transformation -- nth-order rogue-wave solutions; Optics -- Periodicals; 535
• DOI: 10.1080/09500340.2016.1177617
• Languages: English
• ISSNs: 0950-0340

Abstract

Abstract : In this paper, we investigate the rogue waves for an integrable coupled nonlinear Schrödinger (CNLS) system with the self-phase modulation, cross-phase modulation and four-wave mixing term, which can describe the propagation of optical waves in a multi-mode fibre. We construct a generalized Darboux transformation (GDT) for the CNLS system and find a gauge transformation which converts the Lax pair into the constant-coefficient differential equations. Solving those equations, we can obtain the vector solutions of the Lax pair. Using the GDT, we derive an iterative formula for the n th-order rogue-wave solutions for the CNLS system. We derive the first- and second-order rogue-wave solutions for the CNLS system and analyse the profiles for the rogue waves with respect to the self-phase modulation term a, cross-phase modulation term c and four-wave mixing term b, respectively. The rogue waves become thinner with the increase in the value for the real part of b and that the effect of a or c on the rogue waves is the same as the one of the real part of b .